Miami Heat guard Ray Allen (34) and forward LeBron James stand on the bench in the closing seconds of a 93-90 loss to the Indiana Pacers in Game 5 of the NBA basketball Eastern Conference finals in Indianapolis, Wednesday, May 28, 2014. The Heat lead the series 3-2. (AP Photo/Michael Conroy)

The Cavaliers could be moving closer to signing a player who would become the oldest player to ever wear a Cavs uniform — but also one of the best pure shooters in franchise history.

According to the Boston Globe, which cited a league source, Ray Allen is leaning toward signing with the Cavs, where he would be reunited with LeBron James, his former teammate on the Miami Heat. According to the Associated Press, Allen’s representatives called the report “unfounded” and Allen is undecided on playing next season.

Allen just turned 39. If he signs with the Cavs, he would become the oldest player in franchise history — by two years. The oldest player to appear in a game for the Cavs is Shaquille O’Neal, who was 37 when he played in 53 games for the Cavs in the 2009-10 season.

O’Neal was at the end of his career when he played for the Cavs. Allen is 39, but looks and plays 10 years younger.

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A 10-time All-Star, Allen has attempted and made more 3-point field goals than any player in NBA history. His .894 career free-throw percentage ranks third among active players and sixth in NBA history.

Last year with Miami, Allen shot 38 percent from the 3-point line and 91 percent from the free throw line while averaging 12.8 minutes per game as the perimeter catch-and-shoot specialist for the Heat. Over the last four seasons, he has shot 42 percent from behind the arc. In the playoffs last season, he was a 42 percent 3-point shooter and shot 92 percent from the free-throw line.

The addition of Allen, and Mike Miller, another perimeter sharp-shooter who played with James in Miami, would give the Cavs the outside threats to discourage double teams when James and/or Kyrie Irving drive the lane. Miller reportedly turned down a three-year, $12 million offer from the Denver Nuggets to sign a two-year, $5.5 million deal with the Cavs.

“Obviously, it’s always tough passing up money, but at the end of the day, being able to team up with LeBron again and getting the chance to win a championship again was too much to pass up,” said Miller recently on ESPN radio.

The Cavs have also reportedly agreed to a one-year deal with another aging ex-Heat perimeter shooter in James Jones. Allen is 39, Miller 34, and Jones 33.

“With LeBron, you are going to win 55 to 60 games regardless,” Miller told ESPN radio. “Now it’s about what you do in the playoffs. For us, even with the young talent that (the Cavs) have there, you’ve got to bring guys that have been there before, even if they are not giving you heavy minutes. ... We’re moving Miami to Northeast Ohio.”